Multicenter, two-part, randomized, Phase I/II, AIDS Clinical Trial Group (ACTG) study of zidovudine (ZDV) alone versus the combination of ZDV and didanosine (ddI) for the treatment of infants less than or equal to 90 days of age or less than or equal to 120 days of age who have symptomatic HIV infection, or are at risk for rapid disease progression (CD4 T-Cell count <1750 cells/mm or <40% total lymphocytes or a positive PCR or culture result within the first 7 days of life). Pharmacokinetic, safety and acute toxicity data for ddI and the combination of ddI and ZDV will be obtained. As part of the phase II part of the study, long-term safety, toxicity and tolerability, as well as anti-HIV activity, will be monitored. Antiviral activity will be assessed by quantitative viral cultures. The study will attempt to establish the rates of development of resistance to both ddI and ZDV, and correlate resistance with clinical and laboratory measures of antiviral activity.